[PDF] Top 20 Global Estimation of the Cauchy Problem Solutions' and Blow up the Navier-Stokes Equation

... smooth solutions always exist, or that if they do exist, they have bounded energy per unit ...this problem one of its seven Millennium Prize problems in ...scattering problem,and this is then used to ... See full document

... scattering problem with the Cauchy problem for the Navier-Stokes ...scattering problem, and this is then used to estimate of solutions of the Cauchy problem ... See full document

... The diffusion process is one of the important processes in mathematical theories and real world problems [–]. The diffusion and/or the boundary conditions have the ten- dency to decrease or increase the solution []. ... See full document

... into global solutions, for some initial data wave breaking ...new global existence result and several new blow-up results of strong solutions for the Cauchy problem ... See full document

... of estimation for them. These methods of estimation are ap- proved by solving the Cauchy problem for equ- ations of viscous incompressible ... See full document

... the global weak solutions for the isentropic fluids for large initial ...the Cauchy problem of the Navier-Stokes equations for viscous compressible barotropic flows in two or three ... See full document

... of blow-up solutions to the 3D incompressible Euler, or Navier-Stokes, equations which arise from smooth initial data with finite kinetic energy is one of the most important problems in ... See full document

... come up with the global well-posed solution of the proof for the incompressible Boussinesq equa- tions in ...the equation was not viscous, such as µ κ = = 0 , Dongho Chae and Hee-Seok Nam [4] studied ... See full document

... Boussinessq equation is a coupling of the fluid velocity field and the temperature ...sible Navier-Stokes and Euler equations, with similar vortex stretching mechan- ism to 3D incompressible ...the ... See full document

... the global existence and large time behavior of weak solutions was studied by Perepelitsa in ...the global well-posedness of the classical solution to the periodic problem with large initial ... See full document

... the Cauchy problem of a weakly dissipative generalized periodic Degasperis-Procesi ...precise blow-up scenarios of strong solutions to the equation are derived by a direct ...the ... See full document

... L R ; let q be a bounded fast-decreasing function. The operator H is called the Schrödinger operator. We consider the three-dimensional inverse scattering problem for the Schrödinger operator, i.e, the scattering ... See full document

... time estimation of the Cauchy problem solution for the Navier-Stokes equations is ...classical solutions for the Navi- er-Stokes ... See full document

... incompressible Navier-Stokes equation with null initial conditions or simply null Navier-Stokes equation was developed from the incompressible Navier-Stokes ... See full document

... the global weak solution for the Camassa-Holm and Degasperis-Procesi ...the global weak solutions of the Camassa-Holm model have been proved by Constantin and Escher [] and Danchin [, ] by ... See full document

... that Navier-Stokes equation enter some class as it was already proved D ( e ; τ A H r ) in ar- bitrarily short ...the Navier-Stokes equation on the ... See full document

... ZY: Global weak solutions for the Novikov ...the Cauchy problem for the Novikov ...The Cauchy problem for the integrable Novikov ...The Cauchy problem for the ... See full document

... Boussinesq-type equation, which describes the bidirectional propagation of small amplitude and long capillary gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but ... See full document

... is global with energy which decays exponentially under the potential ...time blow-up for solutions starting in the unstable set is proved, but also under some appropriate assumptions on g and ... See full document

... should guarantee the smoothness of u. This is indeed the case and was confirmed in [2], [4]. Many efforts have been made to refine (7), see e.g. [1], [6], [10], [14], [15], [17], [23], [24]. It is worth mentioning that ... See full document